s-Wave component of the ground-state electron density in the Hookean model compared with the helium atom

From the exact ground-state wave function of the two-electron Hookean atom, in which the Coulombic repulsion energy e2/r12 between electrons 1 and 2 at separation r12 is retained but the confinement is harmonic with external potential kr2/2, the s-wave component is extracted for force constant k = 1/4. The radial electron density for this l = 0 component is compared with that for the exact ground-state density, and they are quantitatively very similar. Finally, a linear differential equation is found for the s-wave density and this equation is compared and contrasted with the known result for the exact case.